Construct Non-Hierarchical P/NBD Model for CD-Now Transaction Data

In this workbook we construct the non-hierarchical P/NBD models on the CD-NOW transaction data.

1 Load and Construct Datasets

1.1 Load CD-NOW Transaction Data

We now want to load the CD-NOW transaction data.

Code

customer_cohortdata_tbl <- read_rds("data/cdnow_customer_cohort_data_tbl.rds")
customer_cohortdata_tbl |> glimpse()

Rows: 23,570
Columns: 5
$ customer_id     <chr> "00001", "00002", "00003", "00004", "00005", "00006", …
$ cohort_qtr      <chr> "1997 Q1", "1997 Q1", "1997 Q1", "1997 Q1", "1997 Q1",…
$ cohort_ym       <chr> "1997 01", "1997 01", "1997 01", "1997 01", "1997 01",…
$ first_tnx_date  <date> 1997-01-01, 1997-01-12, 1997-01-02, 1997-01-01, 1997-…
$ total_tnx_count <int> 1, 2, 6, 4, 11, 1, 3, 8, 3, 1, 4, 1, 1, 1, 1, 4, 1, 1,…

Code

customer_transactions_tbl <- read_rds("data/cdnow_transaction_data_tbl.rds")
customer_transactions_tbl |> glimpse()

Rows: 69,659
Columns: 8
$ customer_id   <fct> 00001, 00002, 00002, 00003, 00003, 00003, 00003, 00003, …
$ tnx_date      <date> 1997-01-01, 1997-01-12, 1997-01-12, 1997-01-02, 1997-03…
$ tnx_timestamp <dttm> 1997-01-01 21:57:19, 1997-01-12 06:52:02, 1997-01-12 22…
$ tnx_dow       <fct> Wed, Sun, Sun, Thu, Sun, Wed, Sat, Tue, Thu, Wed, Sat, S…
$ tnx_month     <fct> Jan, Jan, Jan, Jan, Mar, Apr, Nov, Nov, May, Jan, Jan, A…
$ tnx_week      <chr> "00", "01", "01", "00", "12", "13", "45", "47", "21", "0…
$ cd_count      <int> 1, 5, 1, 2, 2, 2, 5, 4, 1, 2, 2, 1, 2, 2, 1, 3, 3, 3, 2,…
$ total_spend   <dbl> 11.77, 77.00, 12.00, 20.76, 20.76, 19.54, 57.45, 20.96, …

Code

customer_subset_id <- read_rds("data/cdnow_customer_subset_ids.rds")
customer_subset_id |> glimpse()

 Factor w/ 23570 levels "00030","00029",..: 14 18 61 64 76 81 96 162 164 202 ...

We re-produce the visualisation of the transaction times we used in previous workbooks.

Code

plot_tbl <- customer_transactions_tbl |>
  group_nest(customer_id, .key = "cust_data") |>
  filter(map_int(cust_data, nrow) > 3) |>
  slice_sample(n = 30) |>
  unnest(cust_data)

ggplot(plot_tbl, aes(x = tnx_timestamp, y = customer_id)) +
  geom_line() +
  geom_point() +
  labs(
      x = "Date",
      y = "Customer ID",
      title = "Visualisation of Customer Transaction Times"
    ) +
  theme(axis.text.y = element_text(size = 10))

1.2 Load Derived Data

Code

obs_fitdata_tbl   <- read_rds("data/cdnow_obs_fitdata_tbl.rds")
obs_validdata_tbl <- read_rds("data/cdnow_obs_validdata_tbl.rds")

customer_fit_stats_tbl <- obs_fitdata_tbl |>
  rename(x = tnx_count)

1.3 Load Subset Data

We also want to construct our data subsets for the purposes of speeding up our valuations.

Code

customer_fit_subset_tbl <- obs_fitdata_tbl |>
  filter(customer_id %in% customer_subset_id)

customer_fit_subset_tbl |> glimpse()

Rows: 1,000
Columns: 6
$ customer_id    <fct> 00233, 00181, 00131, 00144, 00080, 00149, 00105, 00172,…
$ first_tnx_date <dttm> 1997-01-01 00:53:10, 1997-01-01 01:22:45, 1997-01-01 0…
$ last_tnx_date  <dttm> 1997-01-01 00:53:10, 1997-01-01 01:22:45, 1997-01-01 0…
$ tnx_count      <dbl> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 1, 0…
$ t_x            <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 3.244…
$ T_cal          <dbl> 52.13758, 52.13465, 52.10480, 52.10328, 52.09607, 52.09…

Code

customer_valid_subset_tbl <- obs_validdata_tbl |>
  filter(customer_id %in% customer_subset_id)

customer_valid_subset_tbl |> glimpse()

Rows: 1,000
Columns: 3
$ customer_id       <fct> 00233, 00181, 00131, 00144, 00080, 00149, 00105, 001…
$ tnx_count         <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0…
$ tnx_last_interval <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 20.68985…

We now use these datasets to set the start and end dates for our various validation methods.

Code

dates_lst <- read_rds("data/cdnow_simulation_dates.rds")

use_fit_start_date <- dates_lst$use_fit_start_date
use_fit_end_date   <- dates_lst$use_fit_end_date

use_valid_start_date <- dates_lst$use_valid_start_date
use_valid_end_date   <- dates_lst$use_valid_end_date

We now split out the transaction data into fit and validation datasets.

Code

customer_fit_transactions_tbl <- customer_transactions_tbl |>
  filter(
    customer_id %in% customer_subset_id,
    tnx_timestamp >= use_fit_start_date,
    tnx_timestamp <= use_fit_end_date
    )
  
customer_fit_transactions_tbl |> glimpse()

Rows: 2,281
Columns: 8
$ customer_id   <fct> 00013, 00016, 00016, 00016, 00016, 00080, 00105, 00131, …
$ tnx_date      <date> 1997-01-01, 1997-01-01, 1997-07-13, 1997-07-26, 1997-09…
$ tnx_timestamp <dttm> 1997-01-01 22:58:54, 1997-01-01 23:18:11, 1997-07-13 14…
$ tnx_dow       <fct> Wed, Wed, Sun, Sat, Wed, Wed, Wed, Wed, Wed, Wed, Fri, W…
$ tnx_month     <fct> Jan, Jan, Jul, Jul, Sep, Jan, Jan, Jan, Jan, Jan, Jan, J…
$ tnx_week      <chr> "00", "00", "27", "29", "36", "00", "00", "00", "00", "0…
$ cd_count      <int> 4, 1, 2, 4, 1, 4, 3, 2, 2, 4, 4, 1, 5, 3, 1, 1, 1, 2, 1,…
$ total_spend   <dbl> 72.94, 9.77, 31.60, 28.51, 9.99, 43.46, 35.31, 30.32, 30…

Code

customer_valid_transactions_tbl <- customer_transactions_tbl |>
  filter(
    customer_id %in% customer_subset_id,
    tnx_timestamp >= use_valid_start_date,
    tnx_timestamp <= use_valid_end_date
    )
  
customer_valid_transactions_tbl |> glimpse()

Rows: 473
Columns: 8
$ customer_id   <fct> 00360, 00360, 00360, 00559, 00663, 00663, 00663, 00663, …
$ tnx_date      <date> 1998-02-12, 1998-05-01, 1998-05-25, 1998-06-01, 1998-03…
$ tnx_timestamp <dttm> 1998-02-12 07:30:09, 1998-05-01 23:41:09, 1998-05-25 19…
$ tnx_dow       <fct> Thu, Fri, Mon, Mon, Mon, Tue, Thu, Sun, Mon, Fri, Mon, S…
$ tnx_month     <fct> Feb, May, May, Jun, Mar, Apr, May, May, Jun, Jun, Jun, F…
$ tnx_week      <chr> "06", "17", "21", "22", "13", "17", "18", "18", "24", "2…
$ cd_count      <int> 1, 1, 2, 4, 3, 3, 1, 1, 1, 2, 2, 2, 2, 1, 2, 4, 8, 4, 8,…
$ total_spend   <dbl> 11.49, 11.49, 23.87, 54.85, 27.47, 36.97, 11.88, 9.49, 1…

Finally, we want to extract the first transaction for each customer, so we can add this data to assess our models.

Code

customer_initial_tnx_tbl <- customer_fit_transactions_tbl |>
  slice_min(n = 1, order_by = tnx_timestamp, by = customer_id)

customer_initial_tnx_tbl |> glimpse()

Rows: 1,000
Columns: 8
$ customer_id   <fct> 00013, 00016, 00080, 00105, 00131, 00144, 00149, 00168, …
$ tnx_date      <date> 1997-01-01, 1997-01-01, 1997-01-01, 1997-01-01, 1997-01…
$ tnx_timestamp <dttm> 1997-01-01 22:58:54, 1997-01-01 23:18:11, 1997-01-01 07…
$ tnx_dow       <fct> Wed, Wed, Wed, Wed, Wed, Wed, Wed, Wed, Wed, Wed, Wed, T…
$ tnx_month     <fct> Jan, Jan, Jan, Jan, Jan, Jan, Jan, Jan, Jan, Jan, Jan, J…
$ tnx_week      <chr> "00", "00", "00", "00", "00", "00", "00", "00", "00", "0…
$ cd_count      <int> 4, 1, 4, 3, 2, 2, 4, 1, 5, 3, 1, 1, 1, 2, 1, 2, 1, 1, 2,…
$ total_spend   <dbl> 72.94, 9.77, 43.46, 35.31, 30.32, 30.72, 54.87, 14.96, 5…

We now expand out these initial transactions so that we can append them to our simulations.

Code

sim_init_tbl <- customer_initial_tnx_tbl |>
  transmute(
    customer_id,
    draw_id       = list(1:n_sim),
    tnx_timestamp,
    tnx_amount    = total_spend
    ) |>
  unnest(draw_id)

sim_init_tbl |> glimpse()

Rows: 2,000,000
Columns: 4
$ customer_id   <fct> 00013, 00013, 00013, 00013, 00013, 00013, 00013, 00013, …
$ draw_id       <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1…
$ tnx_timestamp <dttm> 1997-01-01 22:58:54, 1997-01-01 22:58:54, 1997-01-01 22…
$ tnx_amount    <dbl> 72.94, 72.94, 72.94, 72.94, 72.94, 72.94, 72.94, 72.94, …

Before we start on that, we set a few parameters for the workbook to organise our Stan code.

Code

stan_modeldir <- "stan_models"
stan_codedir  <-   "stan_code"

2 Fit First P/NBD Model

We now construct our Stan model and prepare to fit it with our synthetic dataset.

We also want to set a number of overall parameters for this workbook

To start the fit data, we want to use the 1,000 customers. We also need to calculate the summary statistics for the validation period.

2.1 Compile and Fit Stan Model

We now compile this model using CmdStanR.

Code

pnbd_fixed_stanmodel <- cmdstan_model(
  "stan_code/pnbd_fixed.stan",
  include_paths =   stan_codedir,
  pedantic      =           TRUE,
  dir           =  stan_modeldir
  )

We then use this compiled model with our data to produce a fit of the data.

Code

stan_modelname <- "pnbd_cdnow_fixed1"
stanfit_seed   <- stanfit_seed + 1
stanfit_prefix <- str_c("fit_", stan_modelname) 

stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")

stan_data_lst <- customer_fit_stats_tbl |>
  select(customer_id, x, t_x, T_cal) |>
  compose_data(
    lambda_mn = 0.25,
    lambda_cv = 1.00,
    
    mu_mn     = 0.10,
    mu_cv     = 1.00,
    )

if(!file_exists(stanfit_object_file)) {
  pnbd_cdnow_fixed1_stanfit <- pnbd_fixed_stanmodel$sample(
    data            =                stan_data_lst,
    chains          =                            4,
    iter_warmup     =                          500,
    iter_sampling   =                          500,
    seed            =                 stanfit_seed,
    save_warmup     =                         TRUE,
    output_dir      =                stan_modeldir,
    output_basename =               stanfit_prefix,
    )
  
  pnbd_cdnow_fixed1_stanfit$save_object(stanfit_object_file, compress = "gzip")

} else {
  message(glue("Found file {stanfit_object_file}. Loading..."))
  
  pnbd_cdnow_fixed1_stanfit <- read_rds(stanfit_object_file)
}

pnbd_cdnow_fixed1_stanfit$print()

  variable       mean     median     sd    mad         q5        q95 rhat
 lp__      -287237.83 -287236.00 171.62 171.24 -287522.10 -286953.95 1.00
 lambda[1]       0.14       0.11   0.11   0.08       0.02       0.36 1.00
 lambda[2]       0.20       0.20   0.06   0.06       0.11       0.31 1.00
 lambda[3]       0.08       0.07   0.04   0.04       0.03       0.15 1.01
 lambda[4]       0.04       0.03   0.02   0.02       0.01       0.08 1.00
 lambda[5]       0.06       0.05   0.05   0.04       0.01       0.16 1.00
 lambda[6]       0.17       0.15   0.11   0.10       0.04       0.40 1.00
 lambda[7]       0.05       0.05   0.03   0.03       0.01       0.11 1.00
 lambda[8]       0.07       0.06   0.04   0.03       0.02       0.14 1.00
 lambda[9]       0.14       0.08   0.16   0.09       0.00       0.44 1.00
 ess_bulk ess_tail
      718     1070
     2775     1176
     3942     1256
     2854     1181
     3001     1089
     3151     1140
     2636     1184
     3394     1382
     3972     1245
     2078      982

 # showing 10 of 70711 rows (change via 'max_rows' argument or 'cmdstanr_max_rows' option)

We have some basic HMC-based validity statistics we can check.

Code

pnbd_cdnow_fixed1_stanfit$cmdstan_diagnose()

Processing csv files: /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed1-1.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed1-2.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed1-3.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed1-4.csvWarning: non-fatal error reading adaptation data


Checking sampler transitions treedepth.
Treedepth satisfactory for all transitions.

Checking sampler transitions for divergences.
No divergent transitions found.

Checking E-BFMI - sampler transitions HMC potential energy.
E-BFMI satisfactory.

Effective sample size satisfactory.

Split R-hat values satisfactory all parameters.

Processing complete, no problems detected.

2.2 Visual Diagnostics of the Sample Validity

Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.

Code

parameter_subset <- c(
  "lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
  "mu[1]",     "mu[2]",     "mu[3]",     "mu[4]"
  )

pnbd_cdnow_fixed1_stanfit$draws(inc_warmup = FALSE) |>
  mcmc_trace(pars = parameter_subset) +
  expand_limits(y = 0) +
  labs(
    x = "Iteration",
    y = "Value",
    title = "Traceplot of Sample of Lambda and Mu Values"
    ) +
  theme(axis.text.x = element_text(size = 10))

We also check \(N_{eff}\) as a quick diagnostic of the fit.

Code

pnbd_cdnow_fixed1_stanfit |>
  neff_ratio(pars = c("lambda", "mu")) |>
  mcmc_neff() +
    ggtitle("Plot of Parameter Effective Sample Sizes")

Finally, we want to check out the energy diagnostic, which is often indicative of problems with the posterior mixing.

Code

pnbd_cdnow_fixed1_stanfit |>
  nuts_params() |>
  mcmc_nuts_energy(binwidth = 50)

2.3 Assess the Model

As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.

We first run the assessment data.

Code

pnbd_stanfit <- pnbd_cdnow_fixed1_stanfit |>
  recover_types(customer_fit_stats_tbl)

pnbd_cdnow_fixed1_assess_data_lst <- run_model_assessment(
  model_stanfit       = pnbd_stanfit,
  insample_tbl        = customer_fit_subset_tbl,
  fit_label           = "pnbd_cdnow_fixed1",
  fit_end_dttm        = use_fit_end_date     |> as.POSIXct(),
  valid_start_dttm    = use_valid_start_date |> as.POSIXct(),
  valid_end_dttm      = use_valid_end_date   |> as.POSIXct(),
  precompute_rootdir  = "precompute",
  data_dir            = "data",
  summary_include_tnx = FALSE,
  sim_seed            = 2010
  )

pnbd_cdnow_fixed1_assess_data_lst |> glimpse()

List of 5
 $ model_fit_index_filepath     : 'glue' chr "data/pnbd_cdnow_fixed1_assess_fit_index_tbl.rds"
 $ model_valid_index_filepath   : 'glue' chr "data/pnbd_cdnow_fixed1_assess_valid_index_tbl.rds"
 $ model_simstats_filepath      : 'glue' chr "data/pnbd_cdnow_fixed1_assess_model_simstats_tbl.rds"
 $ model_fit_simstats_filepath  : 'glue' chr "data/pnbd_cdnow_fixed1_assess_fit_simstats_tbl.rds"
 $ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_fixed1_assess_valid_simstats_tbl.rds"

2.3.1 Check In-Sample Data Validation

We first check the model against the in-sample data and we need to add back in the initial transactions to the simulation data.

Code

simdata_tbl <- pnbd_cdnow_fixed1_assess_data_lst |>
  use_series(model_fit_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  bind_rows(sim_init_tbl) |>
  arrange(customer_id, draw_id, tnx_timestamp)


assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_fit_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> print()

$total_plot

$quant_plot

Code

#assess_plots_lst |> map(print)

This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.

2.3.2 Check Out-of-Sample Data Validation

We now repeat for the out-of-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed1_assess_data_lst |>
  use_series(model_valid_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  arrange(customer_id, draw_id, tnx_timestamp)


assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_valid_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

3 Fit Alternate Prior Model.

We want to try an alternate prior model with a smaller co-efficient of variation to see what impact it has on our procedures.

Code

stan_modelname <- "pnbd_cdnow_fixed2"
stanfit_seed   <- stanfit_seed + 1
stanfit_prefix <- str_c("fit_", stan_modelname) 

stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")


stan_data_lst <- customer_fit_stats_tbl |>
  select(customer_id, x, t_x, T_cal) |>
  compose_data(
    lambda_mn = 0.25,
    lambda_cv = 0.50,
    
    mu_mn     = 0.10,
    mu_cv     = 0.50,
    )

if(!file_exists(stanfit_object_file)) {
  pnbd_cdnow_fixed2_stanfit <- pnbd_fixed_stanmodel$sample(
    data            =                stan_data_lst,
    chains          =                            4,
    iter_warmup     =                          500,
    iter_sampling   =                          500,
    seed            =                 stanfit_seed,
    save_warmup     =                         TRUE,
    output_dir      =                stan_modeldir,
    output_basename =               stanfit_prefix,
    )

  pnbd_cdnow_fixed2_stanfit$save_object(stanfit_object_file, compress = "gzip")

} else {
  message(glue("Found file {stanfit_object_file}. Loading..."))
  
  pnbd_cdnow_fixed2_stanfit <- read_rds(stanfit_object_file)
}

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Code

pnbd_cdnow_fixed2_stanfit$print()

  variable       mean     median     sd    mad         q5        q95 rhat
 lp__      -703259.38 -703254.00 156.38 149.74 -703528.00 -703010.95 1.01
 lambda[1]       0.19       0.18   0.09   0.09       0.07       0.36 1.00
 lambda[2]       0.22       0.21   0.06   0.06       0.13       0.32 1.00
 lambda[3]       0.11       0.11   0.05   0.04       0.05       0.20 1.00
 lambda[4]       0.07       0.07   0.03   0.03       0.03       0.13 1.00
 lambda[5]       0.13       0.12   0.06   0.05       0.05       0.23 1.00
 lambda[6]       0.21       0.20   0.09   0.08       0.09       0.38 1.00
 lambda[7]       0.09       0.09   0.04   0.04       0.04       0.16 1.01
 lambda[8]       0.10       0.10   0.04   0.04       0.05       0.18 1.01
 lambda[9]       0.21       0.19   0.11   0.10       0.07       0.42 1.00
 ess_bulk ess_tail
      561      978
     3530     1331
     5758     1482
     5335     1400
     3873     1494
     3903     1537
     5179     1270
     4093     1315
     4457     1236
     4523     1522

 # showing 10 of 70711 rows (change via 'max_rows' argument or 'cmdstanr_max_rows' option)

We have some basic HMC-based validity statistics we can check.

Code

pnbd_cdnow_fixed2_stanfit$cmdstan_diagnose()

Processing csv files: /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed2-1.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed2-2.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed2-3.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed2-4.csvWarning: non-fatal error reading adaptation data


Checking sampler transitions treedepth.
Treedepth satisfactory for all transitions.

Checking sampler transitions for divergences.
No divergent transitions found.

Checking E-BFMI - sampler transitions HMC potential energy.
E-BFMI satisfactory.

Effective sample size satisfactory.

Split R-hat values satisfactory all parameters.

Processing complete, no problems detected.

3.1 Visual Diagnostics of the Sample Validity

Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.

Code

parameter_subset <- c(
  "lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
  "mu[1]",     "mu[2]",     "mu[3]",     "mu[4]"
  )

pnbd_cdnow_fixed2_stanfit$draws(inc_warmup = FALSE) |>
  mcmc_trace(pars = parameter_subset) +
  expand_limits(y = 0) +
  labs(
    x = "Iteration",
    y = "Value",
    title = "Traceplot of Sample of Lambda and Mu Values"
    ) +
  theme(axis.text.x = element_text(size = 10))

We want to check the \(N_{eff}\) statistics also.

Code

pnbd_cdnow_fixed2_stanfit |>
  neff_ratio(pars = c("lambda", "mu")) |>
  mcmc_neff() +
    ggtitle("Plot of Parameter Effective Sample Sizes")

Finally, we want to check out the energy diagnostic, which is often indicative of problems with the posterior mixing.

Code

pnbd_cdnow_fixed2_stanfit |>
  nuts_params() |>
  mcmc_nuts_energy(binwidth = 50)

3.2 Assess the Model

As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.

We first run the assessment data.

Code

pnbd_stanfit <- pnbd_cdnow_fixed2_stanfit |>
  recover_types(customer_fit_stats_tbl)

pnbd_cdnow_fixed2_assess_data_lst <- run_model_assessment(
  model_stanfit       = pnbd_stanfit,
  insample_tbl        = customer_fit_subset_tbl,
  fit_label           = "pnbd_cdnow_fixed2",
  fit_end_dttm        = use_fit_end_date     |> as.POSIXct(),
  valid_start_dttm    = use_valid_start_date |> as.POSIXct(),
  valid_end_dttm      = use_valid_end_date   |> as.POSIXct(),
  precompute_rootdir  = "precompute",
  data_dir            = "data",
  summary_include_tnx = FALSE,
  sim_seed            = 2020
  )

pnbd_cdnow_fixed2_assess_data_lst |> glimpse()

List of 5
 $ model_fit_index_filepath     : 'glue' chr "data/pnbd_cdnow_fixed2_assess_fit_index_tbl.rds"
 $ model_valid_index_filepath   : 'glue' chr "data/pnbd_cdnow_fixed2_assess_valid_index_tbl.rds"
 $ model_simstats_filepath      : 'glue' chr "data/pnbd_cdnow_fixed2_assess_model_simstats_tbl.rds"
 $ model_fit_simstats_filepath  : 'glue' chr "data/pnbd_cdnow_fixed2_assess_fit_simstats_tbl.rds"
 $ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_fixed2_assess_valid_simstats_tbl.rds"

3.2.1 Check In-Sample Data Validation

We first check the model against the in-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed2_assess_data_lst |>
  use_series(model_fit_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  bind_rows(sim_init_tbl) |>
  arrange(customer_id, draw_id, tnx_timestamp)


assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_fit_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.

3.2.2 Check Out-of-Sample Data Validation

We now repeat for the out-of-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed2_assess_data_lst |>
  use_series(model_valid_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  arrange(customer_id, draw_id, tnx_timestamp)


assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_valid_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

4 Fit Tight-Lifetime Model

We now want to try a model where we use priors with a tighter coefficient of variation for lifetime but keep the CoV for transaction frequency.

Code

stan_modelname <- "pnbd_cdnow_fixed3"
stanfit_seed   <- stanfit_seed + 1
stanfit_prefix <- str_c("fit_", stan_modelname) 

stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")


stan_data_lst <- customer_fit_stats_tbl |>
  select(customer_id, x, t_x, T_cal) |>
  compose_data(
    lambda_mn = 0.25,
    lambda_cv = 1.00,
    
    mu_mn     = 0.10,
    mu_cv     = 0.50,
    )

if(!file_exists(stanfit_object_file)) {
  pnbd_cdnow_fixed3_stanfit <- pnbd_fixed_stanmodel$sample(
    data            =                stan_data_lst,
    chains          =                            4,
    iter_warmup     =                          500,
    iter_sampling   =                          500,
    seed            =                 stanfit_seed,
    save_warmup     =                         TRUE,
    output_dir      =                stan_modeldir,
    output_basename =               stanfit_prefix,
    )

  pnbd_cdnow_fixed3_stanfit$save_object(stanfit_object_file, compress = "gzip")

} else {
  message(glue("Found file {stanfit_object_file}. Loading..."))
  
  pnbd_cdnow_fixed3_stanfit <- read_rds(stanfit_object_file)
}

Running MCMC with 4 chains, at most 12 in parallel...

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All 4 chains finished successfully.
Mean chain execution time: 964.9 seconds.
Total execution time: 969.5 seconds.

Code

pnbd_cdnow_fixed3_stanfit$print()

  variable       mean     median     sd    mad         q5        q95 rhat
 lp__      -526073.69 -526069.50 161.17 160.86 -526339.05 -525813.95 1.00
 lambda[1]       0.14       0.11   0.11   0.09       0.02       0.35 1.00
 lambda[2]       0.21       0.20   0.06   0.06       0.12       0.33 1.00
 lambda[3]       0.08       0.07   0.04   0.04       0.03       0.15 1.00
 lambda[4]       0.04       0.03   0.02   0.02       0.01       0.08 1.00
 lambda[5]       0.07       0.05   0.05   0.04       0.01       0.16 1.00
 lambda[6]       0.18       0.16   0.11   0.10       0.05       0.38 1.00
 lambda[7]       0.06       0.05   0.03   0.03       0.01       0.12 1.00
 lambda[8]       0.07       0.07   0.03   0.03       0.03       0.13 1.00
 lambda[9]       0.14       0.08   0.17   0.09       0.01       0.46 1.00
 ess_bulk ess_tail
      812     1139
     3584     1143
     3932     1208
     3575     1297
     4111     1320
     3491     1032
     4468     1495
     4124     1139
     3995     1041
     2854     1189

 # showing 10 of 70711 rows (change via 'max_rows' argument or 'cmdstanr_max_rows' option)

We have some basic HMC-based validity statistics we can check.

Code

pnbd_cdnow_fixed3_stanfit$cmdstan_diagnose()

Processing csv files: /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed3-1.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed3-2.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed3-3.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed3-4.csvWarning: non-fatal error reading adaptation data


Checking sampler transitions treedepth.
Treedepth satisfactory for all transitions.

Checking sampler transitions for divergences.
No divergent transitions found.

Checking E-BFMI - sampler transitions HMC potential energy.
E-BFMI satisfactory.

Effective sample size satisfactory.

Split R-hat values satisfactory all parameters.

Processing complete, no problems detected.

4.1 Visual Diagnostics of the Sample Validity

Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.

Code

parameter_subset <- c(
  "lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
  "mu[1]",     "mu[2]",     "mu[3]",     "mu[4]"
  )

pnbd_cdnow_fixed3_stanfit$draws(inc_warmup = FALSE) |>
  mcmc_trace(pars = parameter_subset) +
  expand_limits(y = 0) +
  labs(
    x = "Iteration",
    y = "Value",
    title = "Traceplot of Sample of Lambda and Mu Values"
    ) +
  theme(axis.text.x = element_text(size = 10))

We want to check the \(N_{eff}\) statistics also.

Code

pnbd_cdnow_fixed3_stanfit |>
  neff_ratio(pars = c("lambda", "mu")) |>
  mcmc_neff() +
    ggtitle("Plot of Parameter Effective Sample Sizes")

Finally, we want to check out the energy diagnostic, which is often indicative of problems with the posterior mixing.

Code

pnbd_cdnow_fixed3_stanfit |>
  nuts_params() |>
  mcmc_nuts_energy(binwidth = 50)

4.2 Assess the Model

As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.

We first run the assessment data.

Code

pnbd_stanfit <- pnbd_cdnow_fixed3_stanfit |>
  recover_types(customer_fit_stats_tbl)

pnbd_cdnow_fixed3_assess_data_lst <- run_model_assessment(
  model_stanfit       = pnbd_stanfit,
  insample_tbl        = customer_fit_subset_tbl,
  fit_label           = "pnbd_cdnow_fixed3",
  fit_end_dttm        = use_fit_end_date     |> as.POSIXct(),
  valid_start_dttm    = use_valid_start_date |> as.POSIXct(),
  valid_end_dttm      = use_valid_end_date   |> as.POSIXct(),
  precompute_rootdir  = "precompute",
  data_dir            = "data",
  summary_include_tnx = FALSE,
  sim_seed            = 2030
  )

pnbd_cdnow_fixed3_assess_data_lst |> glimpse()

List of 5
 $ model_fit_index_filepath     : 'glue' chr "data/pnbd_cdnow_fixed3_assess_fit_index_tbl.rds"
 $ model_valid_index_filepath   : 'glue' chr "data/pnbd_cdnow_fixed3_assess_valid_index_tbl.rds"
 $ model_simstats_filepath      : 'glue' chr "data/pnbd_cdnow_fixed3_assess_model_simstats_tbl.rds"
 $ model_fit_simstats_filepath  : 'glue' chr "data/pnbd_cdnow_fixed3_assess_fit_simstats_tbl.rds"
 $ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_fixed3_assess_valid_simstats_tbl.rds"

4.2.1 Check In-Sample Data Validation

We first check the model against the in-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed3_assess_data_lst |>
  use_series(model_fit_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  bind_rows(sim_init_tbl) |>
  arrange(customer_id, draw_id, tnx_timestamp)

assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_fit_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.

4.2.2 Check Out-of-Sample Data Validation

We now repeat for the out-of-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed3_assess_data_lst |>
  use_series(model_valid_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  arrange(customer_id, draw_id, tnx_timestamp)

assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_valid_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

5 Fit Narrow-Short-Lifetime Model

We now want to try a model where we use priors with a tighter coefficient of variation for lifetime but keep the CoV for transaction frequency.

Code

stan_modelname <- "pnbd_cdnow_fixed4"
stanfit_seed   <- stanfit_seed + 1
stanfit_prefix <- str_c("fit_", stan_modelname) 

stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")


stan_data_lst <- customer_fit_stats_tbl |>
  select(customer_id, x, t_x, T_cal) |>
  compose_data(
    lambda_mn = 0.25,
    lambda_cv = 1.00,
    
    mu_mn     = 0.20,
    mu_cv     = 0.30,
    )

if(!file_exists(stanfit_object_file)) {
  pnbd_cdnow_fixed4_stanfit <- pnbd_fixed_stanmodel$sample(
    data            =                stan_data_lst,
    chains          =                            4,
    iter_warmup     =                          500,
    iter_sampling   =                          500,
    seed            =                 stanfit_seed,
    save_warmup     =                         TRUE,
    output_dir      =                stan_modeldir,
    output_basename =               stanfit_prefix,
    )

  pnbd_cdnow_fixed4_stanfit$save_object(stanfit_object_file, compress = "gzip")

} else {
  message(glue("Found file {stanfit_object_file}. Loading..."))
  
  pnbd_cdnow_fixed4_stanfit <- read_rds(stanfit_object_file)
}

Running MCMC with 4 chains, at most 12 in parallel...

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Chain 4 finished in 1304.5 seconds.

All 4 chains finished successfully.
Mean chain execution time: 1255.8 seconds.
Total execution time: 1306.4 seconds.

Code

pnbd_cdnow_fixed4_stanfit$print()

  variable       mean     median     sd    mad         q5        q95 rhat
 lp__      -913046.64 -913043.00 158.00 150.48 -913309.00 -912781.90 1.01
 lambda[1]       0.15       0.12   0.12   0.09       0.02       0.38 1.00
 lambda[2]       0.22       0.21   0.07   0.06       0.12       0.33 1.01
 lambda[3]       0.08       0.08   0.04   0.04       0.03       0.16 1.00
 lambda[4]       0.04       0.03   0.03   0.02       0.01       0.09 1.00
 lambda[5]       0.07       0.06   0.06   0.04       0.01       0.19 1.00
 lambda[6]       0.19       0.16   0.11   0.11       0.05       0.41 1.00
 lambda[7]       0.06       0.05   0.04   0.03       0.02       0.13 1.00
 lambda[8]       0.07       0.07   0.04   0.03       0.03       0.14 1.00
 lambda[9]       0.16       0.10   0.19   0.11       0.01       0.53 1.00
 ess_bulk ess_tail
      578     1033
     4203     1307
     4054     1429
     3811     1138
     2783     1063
     3146     1138
     3996     1509
     3993     1273
     3710     1455
     3221     1271

 # showing 10 of 70711 rows (change via 'max_rows' argument or 'cmdstanr_max_rows' option)

We have some basic HMC-based validity statistics we can check.

Code

pnbd_cdnow_fixed4_stanfit$cmdstan_diagnose()

Processing csv files: /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed4-1.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed4-2.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed4-3.csvWarning: non-fatal error reading adaptation data
, /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_fixed4-4.csvWarning: non-fatal error reading adaptation data


Checking sampler transitions treedepth.
Treedepth satisfactory for all transitions.

Checking sampler transitions for divergences.
No divergent transitions found.

Checking E-BFMI - sampler transitions HMC potential energy.
E-BFMI satisfactory.

Effective sample size satisfactory.

Split R-hat values satisfactory all parameters.

Processing complete, no problems detected.

5.1 Visual Diagnostics of the Sample Validity

Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.

Code

parameter_subset <- c(
  "lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
  "mu[1]",     "mu[2]",     "mu[3]",     "mu[4]"
  )

pnbd_cdnow_fixed4_stanfit$draws(inc_warmup = FALSE) |>
  mcmc_trace(pars = parameter_subset) +
  expand_limits(y = 0) +
  labs(
    x = "Iteration",
    y = "Value",
    title = "Traceplot of Sample of Lambda and Mu Values"
    ) +
  theme(axis.text.x = element_text(size = 10))

We want to check the \(N_{eff}\) statistics also.

Code

pnbd_cdnow_fixed4_stanfit |>
  neff_ratio(pars = c("lambda", "mu")) |>
  mcmc_neff() +
    ggtitle("Plot of Parameter Effective Sample Sizes")

Finally, we want to check out the energy diagnostic, which is often indicative of problems with the posterior mixing.

Code

pnbd_cdnow_fixed4_stanfit |>
  nuts_params() |>
  mcmc_nuts_energy(binwidth = 50)

5.2 Assess the Model

As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.

We first run the assessment data.

Code

pnbd_stanfit <- pnbd_cdnow_fixed4_stanfit |>
  recover_types(customer_fit_stats_tbl)

pnbd_cdnow_fixed4_assess_data_lst <- run_model_assessment(
  model_stanfit       = pnbd_stanfit,
  insample_tbl        = customer_fit_subset_tbl,
  fit_label           = "pnbd_cdnow_fixed4",
  fit_end_dttm        = use_fit_end_date     |> as.POSIXct(),
  valid_start_dttm    = use_valid_start_date |> as.POSIXct(),
  valid_end_dttm      = use_valid_end_date   |> as.POSIXct(),
  precompute_rootdir  = "precompute",
  data_dir            = "data",
  summary_include_tnx = FALSE,
  sim_seed            = 2040
  )

pnbd_cdnow_fixed4_assess_data_lst |> glimpse()

List of 5
 $ model_fit_index_filepath     : 'glue' chr "data/pnbd_cdnow_fixed4_assess_fit_index_tbl.rds"
 $ model_valid_index_filepath   : 'glue' chr "data/pnbd_cdnow_fixed4_assess_valid_index_tbl.rds"
 $ model_simstats_filepath      : 'glue' chr "data/pnbd_cdnow_fixed4_assess_model_simstats_tbl.rds"
 $ model_fit_simstats_filepath  : 'glue' chr "data/pnbd_cdnow_fixed4_assess_fit_simstats_tbl.rds"
 $ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_fixed4_assess_valid_simstats_tbl.rds"

5.2.1 Check In-Sample Data Validation

We first check the model against the in-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed4_assess_data_lst |>
  use_series(model_fit_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  bind_rows(sim_init_tbl) |>
  arrange(customer_id, draw_id, tnx_timestamp)


assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_fit_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.

5.2.2 Check Out-of-Sample Data Validation

We now repeat for the out-of-sample data.

Code

simdata_tbl <- pnbd_cdnow_fixed4_assess_data_lst |>
  use_series(model_valid_index_filepath) |>
  read_rds() |>
  use_series(sim_file) |>
  map_dfr(read_rds) |>
  select(customer_id, draw_id, sim_data) |>
  unnest(sim_data) |>
  arrange(customer_id, draw_id, tnx_timestamp)

assess_plots_lst <- create_model_assessment_plots(
  obsdata_tbl = customer_valid_transactions_tbl,
  simdata_tbl = simdata_tbl
  )

assess_plots_lst |> map(print)

$total_plot

$quant_plot

6 Compare Model Outputs

We have looked at each of the models individually, but it is also worth looking at each of the models as a group.

We now want to combine both the fit and valid transaction sets to calculate the summary statistics for both.

Code

obs_summstats_tbl <- list(
    fit   = customer_fit_transactions_tbl,
    valid = customer_valid_transactions_tbl
    ) |>
  bind_rows(.id = "assess_type") |>
  group_by(assess_type) |>
  calculate_transaction_summary_statistics() |>
  pivot_longer(
    cols      = !assess_type,
    names_to  = "label",
    values_to = "obs_value"
    )

obs_summstats_tbl |> glimpse()

Rows: 16
Columns: 3
$ assess_type <chr> "fit", "fit", "fit", "fit", "fit", "fit", "fit", "fit", "v…
$ label       <chr> "p10", "p25", "p50", "p75", "p90", "p99", "total_count", "…
$ obs_value   <dbl> 1.000000, 1.000000, 1.000000, 3.000000, 4.100000, 14.00000…

Code

model_assess_transactions_tbl <- dir_ls("data", regexp = "pnbd_cdnow_fixed.*_assess_.*index") |>
  enframe(name = NULL, value = "file_path") |>
  mutate(
    model_label = str_replace(file_path, "data/pnbd_cdnow_(.*?)_assess_.*", "\\1"),
    assess_type = if_else(str_detect(file_path, "_assess_fit_"), "fit", "valid"),
    
    assess_data = map(
      file_path, construct_model_assessment_data,
      
      .progress = "construct_assess_data"
      )
    ) |>
  select(model_label, assess_type, assess_data) |>
  unnest(assess_data)

model_assess_transactions_tbl |> glimpse()

Rows: 16,129,243
Columns: 6
$ model_label   <chr> "fixed1", "fixed1", "fixed1", "fixed1", "fixed1", "fixed…
$ assess_type   <chr> "fit", "fit", "fit", "fit", "fit", "fit", "fit", "fit", …
$ customer_id   <fct> 00233, 00233, 00233, 00233, 00233, 00233, 00233, 00233, …
$ draw_id       <int> 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5,…
$ tnx_timestamp <dttm> 1997-01-07 17:19:02, 1997-01-08 05:04:59, 1997-01-11 17…
$ tnx_amount    <dbl> 647.50, 59.53, 9.24, 3.45, 33.03, 82.41, 35.28, 2.12, 10…

We now want to calculate the transaction statistics on this full dataset, for each separate draw.

Code

model_assess_tbl <- model_assess_transactions_tbl |>
  group_by(model_label, assess_type, draw_id) |>
  calculate_transaction_summary_statistics()

model_assess_tbl |> glimpse()

Rows: 16,000
Columns: 11
$ model_label <chr> "fixed1", "fixed1", "fixed1", "fixed1", "fixed1", "fixed1"…
$ assess_type <chr> "fit", "fit", "fit", "fit", "fit", "fit", "fit", "fit", "f…
$ draw_id     <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,…
$ p10         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ p25         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ p50         <dbl> 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2…
$ p75         <dbl> 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5…
$ p90         <dbl> 9.0, 8.1, 8.5, 8.0, 8.0, 8.0, 9.0, 8.0, 9.0, 8.0, 8.0, 9.3…
$ p99         <dbl> 30.92, 21.91, 21.55, 22.60, 21.16, 20.00, 20.00, 27.00, 19…
$ total_count <int> 2313, 1946, 2184, 2073, 2058, 1980, 2199, 2199, 1998, 2058…
$ mean_count  <dbl> 4.307263, 3.815686, 4.000000, 3.831793, 3.790055, 3.659889…

We now combine all this data to create a number of different comparison plots for the various summary statistics.

Code

#! echo: TRUE

create_multiple_model_assessment_plot(
  obs_summstats_tbl, model_assess_tbl,
  "total_count", "Total Transactions"
  )

Code

create_multiple_model_assessment_plot(
  obs_summstats_tbl, model_assess_tbl,
  "mean_count", "Average Transactions per Customer"
  )

Code

create_multiple_model_assessment_plot(
  obs_summstats_tbl, model_assess_tbl,
  "p99", "99th Percentile Count"
  )

6.1 Write Assessment Data to Disk

We now want to save the assessment data to disk.

Code

model_assess_tbl |> write_rds("data/assess_data_pnbd_cdnow_fixed_tbl.rds")

R Environment

Code

options(width = 120L)
sessioninfo::session_info()

─ Session info ───────────────────────────────────────────────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.3.1 (2023-06-16)
 os       Ubuntu 22.04.3 LTS
 system   x86_64, linux-gnu
 ui       X11
 language (EN)
 collate  en_US.UTF-8
 ctype    en_US.UTF-8
 tz       Europe/Dublin
 date     2023-12-07
 pandoc   3.1.1 @ /usr/local/bin/ (via rmarkdown)

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 [1] /usr/local/lib/R/site-library
 [2] /usr/local/lib/R/library

──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

Code

options(width = 80L)